I meant to reply to you but hope this helps everyone.
So I had the same problem and contacted Apple and the first fix did not work. Contacted them a second time and after a long session and a determined Apple employee it appears it is fixed. I have a 2015 Ford Escape and iTunes/Apple music would not start or when it did if I got a phone call it would not play when I hung up or when I tried to change to another song or artist. I tried many master resets on the car. unfortunately there are no new updates for my Ford SYNC. Here is what worked.
Open general settings on your phone and go to iPhone storage. Then go to music a
and see if you have any songs stored, mine said zero. The Apple employee had me move a song or album purchased from Apple Music/iTunes to storage. Then turn your phone off and restart, hook it up to your car and see. Mine now is very responsive and works the way it did on iOS 14. Also works like my iPod I had before this phone.